College Physics 10th Edition by Raymond Serway,Chris Vuille

Exercise 81

Figure P23.28 shows a curved surface separating a material with index of refraction n 1 from a material with index n 2. The surface forms an image I of object O. The ray shown in red passes through the surface along a radial line. Its angles of incidence and refraction are both zero, so its direction does not change at the surface. For the ray shown in blue, the direction changes according to n 1 sin 1 = n 2 sin 2. For paraxial rays, we assume 1 and 2 are small, so we may write n 1 tan 1 = n 2 tan 2. The magnification is defined as M = h / h. Prove that the magnification is given by M = n 1 q / n 2 p.